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Gullberg J. — Mathematics: from the birth of numbers
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Название: Mathematics: from the birth of numbersАвтор: Gullberg J. Аннотация: A gently guided, profusely illustrated Grand Tour of the world of mathematics. This extraordinary work takes the reader on a long and fascinating journey — from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous asides, ranging from limericks and tall stories to cartoons and decorative drawings. Over 1000 technical illustrations and cartoons and drawings
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 1110Добавлена в каталог: 22.11.2014Операции: Положить на полку |
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Предметный указатель
Principle, duality, Boolean algebra 253 Principle, duality, projective geometry 434 Principle, Heisenberg’s uncertainty 906 Principle, multiplication 186 Principle, two-value 220 Principle, uncertainty, Heisenberg’s 906 PRISCUS, T. 18 Prism/prisms 400 Prism/prisms, formulas 451 Prism/prisms, height 400 Prism/prisms, truncated 400 Prism/prisms, volume 446 probability 961 Probability, conditional 966 Probability, density function 971 Probability, history 963 979 Probability, mathematical 966 Problem, brachistochrone 590 Problem, Delian 421 Problem, four-color map (theorem) 203 Proclus 366 Product/products 118 Product/products, approximate values 163 Product/products, boundary values 166 Product/products, complex numbers 130 790 Product/products, conversion from sums of functions, derivative 690 Product/products, determinants 650 Product/products, Euler 778 Product/products, indeterminate 785 Product/products, scalar 614 Product/products, sets 241 Product/products, symbol 105 Product/products, tree 186 Product/products, trigonometric, breaking up 514 Product/products, triple, scalar 622 Product/products, triple, vector 623 Product/products, vector 617 Projectile, path 589 901 Projection 373 Projection matrix 658 Projection, Mercator 396 Projective geometry 377 Projective geometry, Mercator projection 396 Prolate ellipsoid 405 Proof by deduction 158 Proof by induction 158 Proof by reductio ad absurdum 159 Proof/proofs, computer generated 160 204 333 Proof/proofs, direct, symbolic logic 227 Proof/proofs, indirect 159 Proof/proofs, indirect, symbolic logic 227 Proof/proofs, mathematical 157 Proper fractions 74 Proper subset 237 Properties, commutative, vectors 615 619 Properties, distributive, vectors 615 Proportion, symbols 110 Proportional, mean 111 Proportionality, constant 349 Proportionality, direct 349 Proportionality, inverse 350 Proportionals 111 Propositions 220 Protolanguage 8 25 Pseudo-primes 80 PTOLEMY (PTOLEMAEUS), history of geometry 366 367 PTOLEMY (PTOLEMAEUS), history of trigonometry 463 PTOLEMY (PTOLEMAEUS), law of sines 480 PTOLEMY (PTOLEMAEUS), motion 894 PTOLEMY (PTOLEMAEUS), theorem of 402 Ptolemy’s theorem 438 Punctum temporis 18 Pure, imaginary numbers 71 Pure, surds 139 Puzzle, fifteen 193 Pyramidal numbers, square 293 Pyramids 400 Pyramids, formulas 451 Pyramids, volume 447 PYTHAGORAS, equations 297 PYTHAGORAS, history of calculus 674 PYTHAGORAS, music 922 Pythagoras, Pythagorean Theorem 435 PYTHAGORAS, reductio ad absurdum 159 Pythagoras’s lute 420 Pythagorean brotherhood 397 Pythagorean doctrine of opposites 291 Pythagorean identities 508 Pythagorean number theorem 332 Pythagorean numbers 332 Pythagorean Theorem 435 Pythagorean triples 332 qed 159 Quadrangle 394 Quadrans 16 Quadrant, astronomical instrument 463 Quadratic equations 309 Quadratic formula 311 Quadratic functions 351 Quadrature formulas 947 Quadrilateral 392 394 Quadrilateral, about a circle 438 Quadrilateral, area 445 Quadrilateral, in a circle 430 Quadrivium 870 Quadrual 4 Quantifier, existential 221 Quantifier, universal 220 Quantity, vector 602 Quart 409 Quartic equations 320 Quaternary 46 Quaternion 601 Quetelet, A. 979 Quinary 46 Quinctilis 19 Quinta essentia 398 Quintic equations 300 Quipu 182 Quotient/quotients 120 Quotient/quotients, approximate values 163 Quotient/quotients, boundary values 166 Quotient/quotients, complex numbers 130 790 Quotient/quotients, derivative 691 Quotient/quotients, indeterminate 784 RAD 410 Radian 410 Radical 138 Radical, simplified form 139 Radicand 138 Radioactive decay 1001 Radiocarbon dating 1002 Radius/radii, circle 391 Radius/radii, circumscribed circles 440 Radius/radii, coordinate system 472 Radius/radii, inscribed circles 440 Radius/radii, radius vector, complex number 788 Radius/radii, sphere 403 Radius/radii, vector 576 Rahn, J.H. 105 135 Random numbers 967 Random variable 971 Range/ranges, functions 339 342 505 Range/ranges, measure of dispersion 976 Range/ranges, trigonometric functions 505 Rank, matrix 664 Ratio, common, series 264 Ratio, golden 418 Ratio, symbols 110 Ratio, test, d’Alambert’s 277 Rational functions 348 Rational numbers 70 72 Rationalizing, denominator 139 Ray/rays 387 Real axis, number plane 788 Real numbers 70 Real zeros, methods of approximation 931 RECORDE, R., abacus 170 RECORDE, R., addition 116 RECORDE, R., equality sign 107 RECORDE, R., multiplication 118 RECORDE, R., plus and minus notations 103 rectangle 395 Rectangle, area 441 Rectangle, golden 419 Rectangular coordinate system 549 Rectilinear motion 896 Recursion formulas, integration 730 Reduced equation 1017 Reductio ad absurdum, proof by 159 Reduction formulas, integration 730 Reentrant angle 392 Reflection, conics, light rays 408 Reflector, ellipsoid 431 Reflector, paraboloid 432 Reflex angle 388 Reflexive law 132 REGIOMONTANUS, J. 103 464 Regula de Tri 111 Regula Falsi 297 Regular decagon, Euclidean construction 416 Regular heptadecagon, Euclidean construction 417 Regular pentadecagon, Euclidean construction 416 Regular pentagon, Euclidean construction 415 Regular polygon/polygons 392 Regular polygons, Euclidean construction 415 Regular polyhedra, theorems 448 450 Regular polyhedron/polyhedra, definitions 397 Regular pyramid 400 REISCH, G. 115 116 218 870 890 922 962 Relative error 161 Relative extrema 799 Relative maximum 341 Relative minimum 341 Relative minimum, derivative 798 Relativity, general theory of 904 Relativity, Special Theory of 904 Reliability, calculations 161 Reliability, digits 161 Reliable digits 162 Remainder, Taylor series 770 Remainder, theorem 303 RENARD, Ch. 929 Replacement, samples with 199 Residue classes 123 Residue classes, complex numbers 137 Resistance 1011 Resisting medium, fall through 1007 Restricted mean-value theorem 717 Restrictions, functions 822 Resultant, vectors 603 605 Results, approximate 161 REUTERSVAERD, O. 374 RHAETICUS, G.J. 464 Rhaeto-Romance number names 21 Rhetorical phase 101 Rhetorical style 298 Rhind papyrus 98 297 RHIND, A.H. 98 Rhodonea 856 Rhombic dodecahedron 399 Rhomboid 394 Rhomboid, area 441 Rhombus/rhombi 394 Rhombus/rhombi, area 441 Rhumb line 596 Richmond, H.W. 417 Riemann geometry 383 Riemann hypothesis 778 Riemann integral 748 Riemann sum 747 Riemann zeta function 778 RIEMANN, G.F.B., definite integral 747 748 RIEMANN, G.F.B., history of geometry 369 RIEMANN, G.F.B., non-Euclidean geometry 383 RIEMANN, G.F.B., zeta function 778 RIENGEL, G. 204 RIESE, A. 113 Right angle 388 Right cone 402 Right cylinder 401 Right prism 400 right triangle 393 Right-hand continuity 358 Right-handed coordinate systems 607 Ring 71 Robert of Chester 49 463 Rod numerals, Chinese 51 RODLER, H. 372 Roget, P.M. 177 Rolle, M. 716 Rolle’s Theorem 716 Roman numerals 6 Roman numeration 39 Roman Republican calendar 18 Romance 20 Romance languages 20 Romanian number names 20 Romansch 21 Root/roots 135 Root/roots, calculation rules 138 Root/roots, complex numbers 793 Root/roots, determining, power series expansion 776 Root/roots, equation/equations 302 313 Root/roots, extraction 141 Root/roots, history 135 Root/roots, index 138 Root/roots, root/coefficient relationships, equations 305 Rotation, orthogonal coordinates 573 Rounding 164 Rounding, errors 165 Rounding, scientific 165 Rounding, shopkeepers’ 165 Row index, determinant 646 Row index, matrix 640 Row operations, elementary 661 Row/rows, matrix 640 Row/rows, target 663 Row/rows, vector 641 Rudolff, C. 135 Ruffini, P. 300 Rule/rules see also "Law" "Formula" "Theorem" Rule/rules of three 111 Rule/rules, chain, derivatives, composite functions 691 Rule/rules, Cramer’s 668 Rule/rules, general power 692 Rule/rules, Guldin’s first 866 Rule/rules, Guldin’s second 884 Rule/rules, L’Hospital’s 782 Rule/rules, power, general 692 Rule/rules, Regula de Tri 111 Rule/rules, rounding 164 Rule/rules, Sarrus’s 647 Rule/rules, Simpson’s 955 957 Rule/rules, trapezoidal 949 Russell, B. 218 235 Russell’s paradox 235 Rutherford, E. 964 Saccheri, G. 369 Saddle point 816
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